Final answer:
To determine the temperature of the furnace, calculate the current using Ohm's Law and apply the known slope of the temperature-current relationship. At 4 V across 500 Ohm, the current is 8 mA. Thus, the measured temperature is 125°C.
Step-by-step explanation:
The student is asking about the process of determining the temperature in a furnace based on the voltage measured across a resistance, given the current output of a temperature transmitter. Since the relationship between measured temperature and the output current is a straight line with a positive slope, we need to apply a simple linear fraction to solve for the temperature.
First, let's define the relationship between the temperature (T), the current (I), and the voltage (V) in the given scenario:
- The transmitter has a range from 0-500°C corresponding to 4-20 mA current output.
- There is a direct relationship between the temperature and current, so the slope of this relationship is (500°C-0°C) / (20 mA - 4 mA) = 31.25°C per mA.
- The resistance (R) used to measure the voltage is 500 Ohm.
Since the voltage (V) across the resistance is given by Ohm's Law V = IR, and a 4 V reading was obtained, the current (I) in the loop can be calculated as:
I = V / R = 4 V / 500 Ω = 0.008 A or 8 mA. To find the corresponding temperature, we consider that 4 mA corresponds to 0°C and 8 mA would correspond to:
T = (8 mA - 4 mA) × 31.25°C/mA = 125°C
Therefore, the temperature of the furnace is 125°C.